Multiquantum integral kinetic equation for the longitudinal complex dielectric function is derived. Heisenberg equation of motion and fluctuation-dissipation theorem has been used to calculate multiplasmon transmission electron energy loss spectra. Strong interaction between high-energy electrons penetrating the solid state and plasma of valence electrons is taken into account. It is shown that average number of high-frequency plasmons generated in every collision process is more than one for typical values of metal parameters. It is obtained that excitation of a good few of plasmons is simultaneous event. Calculated multiplasmon structure of electron energy loss spectra coincides with experimental one.